This code should work with the LEDs wired the original way.
You could even put a time delay before the ON time and after the ON time, to “push” the waveform around. To get the desired timing to get the quasi sine wave at 60 Hz. I have no idea what timing will help!
Just be sure the total adds up to the times for 60Hz.

START:
PAUSEUS 2074 ' before pulse
LOW GPIO.1 ‘ON = pulse
PAUSEUS 4168 ' ON TIME - GPIO.1 only
HIGH GPIO.1 ‘both pins OFF
PAUSEUS 2074 ' after pulse
PAUSEUS 20 ' anti-overlap time
‘should add to 8.336 milliseconds

PAUSEUS 2074 ' before pulse
LOW GPIO.0 ‘ON = pulse
PAUSEUS 4168 ' ON TIME - GPIO.0 only
HIGH GPIO.0 ‘both pins OFF
PAUSEUS 2074 ' after pulse
PAUSEUS 20 ' anti-overlap time
‘should add to 8.336 milliseconds
GOTO START '60 HZ FREQUENCY

END

I still would like to know between which points are you measuring the wave (voltage) from?